Quantum Simulation of Quantized Plasmons in 1D Systems: The critical role of on-site repulsion and Coulomb exchange

Linear atomic chains, such as atom chains on surfaces, linear arrays of dopant atoms in semiconductors, or linear molecules, provide ideal testbeds for studying single-particle, collective (plasmonic) and strongly correlated excitations in the quantum limit for interacting matter systems. We use exact diagonalization to find the many-body excitations of finite (4-26) atom chains, including hopping, long-range electron-electron repulsion and the corresponding electron-core attraction in an extended-range Hubbard model. For spinless electrons, we showed previously that quantized plasmonic excitations can be identified in chains as short as 8 atoms and can be launched one-by-one by quantum emitters attached to the chain. When spin is included, we find that quantized plasmons still can exist in short chains for a wide range of on-site repulsion of opposite spins U. However, for U large enough that the same spins cluster locally, the excitations cease to be plasmonic. Short range Coulomb exchange also plays a key role. Quantized plasmonic excitations disappear in the absence of this exchange. Systems with and without spin will be compared to highlight the essential physics that determines the quantization of 1D excitations in each regime.